Let be a function given by where . If is continuous at , then is equal to :

Question

Let  be a function given by  where . If  is continuous at , then  is equal to :

Canvas Classes · Accepted Answer

🧠 Two Standard Limits, One Continuity Equation

This is another continuity-at-a-point problem with three pieces. Same plan as always: compute LHL from the  piece, set equal to  (the value at 0), compute RHL from the  piece, set equal to .

Look at each piece. The left piece  should ring a bell. The identity  converts it instantly into , which is . The right piece has , and again  does the conversion.

The habit I want you to build: whenever you see , immediately rewrite it as twice a sine squar

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